CLASS 10TH - MATH UNIT TEST SOLVED PREM SIR

📘 UNIT TEST – X MATHS (SET-B)
Solved by Prem Sir

📞 Contact: 6200409895

Q1. Find the HCF of smallest prime and smallest composite numbers. (2)

Baccho ❤️, sabse chhoti prime number hoti hai 2 aur composite hoti hai 4.
Dono ka HCF nikalte hain: HCF(2, 4) = 2 ✅
Yani sahi uttar hai: 2

Q2. Prove that 5 + √3 is an irrational number. (5)

Maan lo 5 + √3 rational hai.
Toh 5 + √3 = a/b ⇒ √3 = a/b - 5 ⇒ rational ban gaya 😵
Par baccho, √3 to irrational hota hai! Galat maan liya.
✅ Isiliye 5 + √3 bhi irrational hai. Proved!

Q3. Solve: x + 20y = 1000 and x + 26y = 1180

Chalo subtract karte hain:
(x + 26y) - (x + 20y) = 180 ⇒ 6y = 180 ⇒ y = 30
Ab y = 30 ko kisi bhi eqn mein daalo:
x + 20×30 = 1000 ⇒ x = 400 ✅
Final Answer: x = 400, y = 30

Q4. Show that 6ⁿ never ends with zero where n is a natural number. (3)

Baccho, kisi bhi number ke last mein 0 tabhi aata hai jab usme 2 aur 5 dono ho.
6 = 2×3 hai, usme 5 nahi hai.
✅ To 6ⁿ kabhi 0 pe end nahi karega. Clear hai?

Q5. Find value of k: x + ky + 5 = 0 and 4x + 8y + 6 = 0 are parallel. (3)

Parallel lines ka matlab slope same honi chahiye:
First eqn: slope = -1/k, Second: slope = -4/8 = -1/2
To -1/k = -1/2 ⇒ k = 2 ✅
Simple logic, done!

Q6. HCF and LCM of two numbers x and y is 5 and 200. Find x × y. (3)

Ek magic formula hota hai: HCF × LCM = x × y
To 5 × 200 = 1000 ✅
Final answer: x × y = 1000